Wide viewing angle reflective display

ABSTRACT

A reflective display having a plurality of approximately hemispherical high refractive index (η 1 ) transparent hemi-beads substantially covering and protruding inwardly from a transparent sheet&#39;s inward surface. The transparent sheet, which has an outward viewing surface, has a refractive index (η 2 ) which can be low (i.e. η 1 ≈1.92 and η 2 ≈1.59). A member is selectably moved into an intense evanescent wave region at the hemi-beads&#39; inward side to selectably frustrate substantial total internal reflection of light rays. The member can be a plurality of light scattering particles suspended in a low refractive index (η 3 ≈1.27) electrophoresis medium and electrophoretically moved into or out of the intense evanescent wave region.

REFERENCE TO RELATED APPLICATION

[0001] This is a division of U.S. patent application Ser. No. 10/086,349filed 4 Mar. 2002.

TECHNICAL FIELD

[0002] This invention improves the angular viewing range of reflectivedisplays.

BACKGROUND

[0003] Images can be displayed by controllably frustrating totalinternal reflection (TIR) to switch selected pixels of a multi-pixeldisplay between a reflective state in which light incident on thosepixels undergoes TIR, and a non-reflective state in which TIR isfrustrated at those pixels. As one example, electrophoresis can be usedto controllably frustrate TIR and selectably switch pixels' states insuch displays. Electrophoresis is a well known phenomenon whereby anapplied electric field moves charged particles, ions or moleculesthrough a medium. An electromagnetic force can be selectively applied tomove particles through an electrophoretic medium toward or away from anevanescent wave region to frustrate TIR at selected pixels. Thisinvention increases the range of practical viewing angles for imagesdisplayed by frustrated TIR or other reflective display methods.

BRIEF DESCRIPTION OF DRAWINGS

[0004]FIG. 1A is a fragmented cross-sectional view, on a greatlyenlarged scale, of a portion of an electrophoretically frustrated TIRdisplay in accordance with one embodiment of the invention.

[0005]FIG. 1B schematically illustrates the wide angle viewing range αof the FIG. 1A apparatus, and the angular range β of the illuminationsource.

[0006]FIG. 2 is a cross-sectional view, on a greatly enlarged scale, ofa hemispherical portion of one of the spherical high refractive indexbeads of the FIG. 1A apparatus.

[0007]FIGS. 3A, 3B and 3C depict semi-retro-reflection of light raysperpendicularly incident on the FIG. 2 hemispherical structure atincreasing off-axis distances at which the incident rays undergo TIRtwo, three and four times respectively.

[0008]FIGS. 4A, 4B, 4C, 4D, 4E, 4F and 4G depict the FIG. 2hemispherical structure, as seen from viewing angles which are offset0°, 15°, 30°, 45°, 60°, 75° and 90° respectively from the perpendicular.

[0009]FIG. 5A graphically depicts the angular deviation from trueretro-reflection of light rays reflected by the FIG. 2 hemisphericalstructure. Angular deviation is shown as a function of off-axis distancea normalized such that the radius r=1. FIG. 5B graphically depicts therelative energy distribution, as a function of angular error, of lightrays reflected by the FIG. 2 hemispherical structure.

[0010]FIGS. 6A and 6B are topographic bottom plan views, on a greatlyenlarged scale, of a plurality of hemispherical (FIG. 6A) andapproximately hemispherical (FIG. 6B) hemi-beads.

[0011]FIGS. 7A and 7B are cross-sectional views, on a greatly enlargedscale, of structures which respectively are not (FIG. 7A) and are (FIG.7B) approximately hemispherical.

[0012]FIGS. 8A through 8F are cross-sectional views, on a greatlyenlarged scale, depicting fabrication of high refractive indexhemispherical structures on a transparent substrate of arbitrarily lowrefractive index.

[0013]FIG. 9 is a fragmented cross-sectional view, on a greatly enlargedscale, of a portion of a display in accordance with an embodiment of theinvention that does not require frustration of TIR.

DESCRIPTION

[0014] Throughout the following description, specific details are setforth in order to provide a more thorough understanding of theinvention. However, the invention may be practiced without theseparticulars. In other instances, well known elements have not been shownor described in detail to avoid unnecessarily obscuring the invention.Accordingly, the specification and drawings are to be regarded in anillustrative, rather than a restrictive, sense.

[0015]FIG. 1A depicts a portion of a front-lit electrophoreticallyfrustrated TIR display 10 having a transparent outward sheet 12 formedby partially embedding a large plurality of high refractive index (η₁)transparent beads 14 in the inward surface of a high refractive index(η₂) polymeric material 16 having a flat outward viewing surface 17which viewer V observes through an angular range of viewing directionsY. The “inward” and “outward” directions are indicated by double-headedarrow Z. Beads 14 are packed closely together to form an inwardlyprojecting monolayer 18 having a thickness approximately equal to thediameter of one of beads 14. Ideally, each one of beads 14 touches allof the beads immediately adjacent to that one bead. As explained below,minimal gaps (ideally, no gaps) remain between adjacent beads. Beads 14may for example be 40-100 micron diameter high index glass beadsavailable from Potters Industries Inc., Valley Forge, Pa, under theproduct classification T-4 Sign Beads. Such beads have a refractiveindex η₁ of approximately 1.90-1.92. Material 14 may be a nano-polymercomposite, for example high refractive index particles suspended in apolymer as described by Kambe et al, in “Refractive Index Engineering ofNano-Polymer Composites”, Materials Research Society Conference, SanFrancisco, Apr. 16-20, 2001 having a comparably high index η₂ (i.e. η₂is greater than about 1.75).

[0016] An electrophoresis medium 20 is maintained adjacent the portionsof beads 14 which protrude inwardly from material 16 by containment ofmedium 20 within a reservoir 22 defined by lower sheet 24. An inert, lowrefractive index (i.e. less than about 1.35), low viscosity,electrically insulating liquid such as Fluorinert™ perfluorinatedhydrocarbon liquid (η₃˜1.27) available from 3M, St. Paul, Minn. is asuitable electrophoresis medium. A bead:liquid TIR interface is thusformed. Medium 20 contains a finely dispersed suspension of lightscattering and/or absorptive particles 26 such as pigments, dyed orotherwise scattering/absorptive silica or latex particles, etc. Sheet24's optical characteristics are relatively unimportant: sheet 24 needonly form a reservoir for containment of electrophoresis medium 20 andparticles 26, and serve as a support for electrode 48 as describedbelow.

[0017] A small critical angle is preferred at the TIR interface sincethis affords a large range of angles over which TIR may occur. Therelatively large ratio of the index of refraction of beads 14(η₁˜1.90-1.92) and material 16 (η₂˜1.92) to that of Fluorinert (η₃˜1.27)yields a critical angle of about 41.4°, which is quite small. In theabsence of electrophoretic activity, as is illustrated to the right ofdashed line 28 in FIG. 1A, a substantial fraction (which may be aslittle as 25%) of the light rays passing through sheet 12 and beads 14undergoes TIR at the inward side of beads 14. For example, incidentlight rays 30, 32 are refracted through material 16 and beads 14. Asdescribed below, the rays undergo TIR two or more times at thebead:liquid TIR interface, as indicated at points 34, 36 in the case ofray 30; and indicated at points 38, 40 in the case of ray 32. Thetotally internally reflected rays are then refracted back through beads14 and material 16 and emerge as rays 42, 44 respectively, achieving a“white” appearance in each reflection region or pixel.

[0018] As is well known, the TIR interface between two media havingdifferent refractive indices is characterized by a critical angle θ_(c).Light rays incident upon the interface at angles less than θ_(c) aretransmitted through the interface. Light rays incident upon theinterface at angles greater than θ_(c) undergo TIR at the interface. Itis also well known that as the angle of an incident light ray approachesθ_(c), the ray is partially reflected by and partially transmittedthrough the TIR interface, with the reflected portion increasing and thetransmitted portion decreasing as the incident angle increases. Thisinvention does not require the incident light rays' angular relationshipto exceed θ_(c) such that the rays undergo “full” TIR. It is sufficient,as is the case for any TIR-type reflective display, for the incidentrays to undergo “substantial TIR” in the sense that a substantialfraction (which may be as little as about 80%) of the incident light isreflected even though the remaining fraction is not reflected; and, itis also sufficient, as is again the case for any TIR-type reflectivedisplay, to frustrate such “substantial TIR”. Persons skilled in the artwill accordingly understand that references herein to “TIR” and to“frustration of TIR” respectively mean “substantial TIR” and“frustration of “substantial TIR”.

[0019] A voltage can be applied across medium 20 via electrodes 46, 48,which can for example be applied by vapour-deposition to the inwardlyprotruding surface portion of beads 14 and to the outward surface ofsheet 24. Electrode 46 is transparent and substantially thin to minimizeits interference with light rays at the bead:liquid TIR interface.Electrode 48 need not be transparent. If electrophoresis medium 20 isactivated by actuating voltage source 50 to apply a voltage betweenelectrodes 46, 48 as illustrated to the left of dashed line 28,suspended particles 26 are electrophoretically moved into the regionwhere the evanescent wave is relatively intense (i.e. within 0.25 micronof the inward surfaces of inwardly protruding beads 14, or closer). Whenelectrophoretically moved as aforesaid, particles 26 scatter or absorblight, by modifying the imaginary and possibly the real component of theeffective refractive index at the bead:liquid TIR interface. This isillustrated by light rays 52, 54 which are scattered and/or absorbed asthey strike particles 26 inside the evanescent wave region at thebead:liquid TIR interface, as indicated at 56, 58 respectively, thusachieving a “dark” appearance in each non-reflective absorption regionor pixel.

[0020] As described above, the net optical characteristics of outwardsheet 12 can be controlled by controlling the voltage applied acrossmedium 20 via electrodes 46, 48. The electrodes can be segmented tocontrol the electrophoretic activation of medium 20 across separateregions or pixels of sheet 12, thus forming an image.

[0021] Besides having the desired low refractive index, perfluorinatedhydrocarbon liquids are also well suited to use in displays formed inaccordance with the invention because they are good electricalinsulators, and they are inert. Perfluorinated hydrocarbon liquids alsohave low viscosity and high density, so particles suspended in suchliquids can be moved electrophoretically relatively easily.

[0022] Beads 14 and polymeric material 16 are preferably opticallyclear—meaning that a substantial fraction of light at normal incidencepasses through a selected thickness of the bead or material, with only asmall fraction of such light being scattered and/or absorbed by the beador material. Diminished optical clarity is caused by such scatteringand/or absorption, typically a combination of both, as the light passesthrough the bead or material. Sheet 12 need only have a thicknessone-half that of beads 14 (i.e. 20 microns for the aforementioned 40micron beads). A material which is “opaque” in bulk form maynevertheless be “optically clear” for purposes of the invention, if a 10micron thickness of such material scatters and/or absorbs only a smallfraction of normal incident light. Some high refractive indexnano-composite polymers have this characteristic and are therefore wellsuited to use in displays formed in accordance with the invention.

[0023] Application of a voltage across medium 20 by means of electrodes46, 48 and voltage source 50 applies electrostatic force on particles26, causing them to move into the evanescent wave region as aforesaid.When particles 26 move into the evanescent wave region they must becapable of frustrating TIR at the bead:liquid interface, by scatteringand/or absorbing the evanescent wave. Although particles 26 may be aslarge as one micron in diameter, the particles' diameter is preferablysignificantly sub-optical (i.e. smaller than about 0.25 microns forvisible light) such that one or more monolayers of particles 26 at theTIR interface can entirely fill the evanescent wave region. Usefulresults are obtained if the diameter of particles 26 is about onemicron, but the display's contrast ratio is reduced because the abilityof particles 26 to pack closely together at the TIR interface is limitedby their diameter. More particularly, near the critical angle, theevanescent wave extends quite far into medium 20, so particles having adiameter of about one micron are able to scatter and/or absorb the waveand thereby frustrate TIR. But, as the angle at which incident lightrays strike the TIR interface increases relative to the critical angle,the depth of the evanescent wave region decreases significantly.Relatively large (i.e. one micron) diameter particles cannot be packedas closely into this reduced depth region and accordingly such particlesare unable to frustrate TIR to the desired extent. Smaller diameter(i.e. 250 mn) particles can however be closely packed into this reduceddepth region and accordingly such particles are able to frustrate TIRfor incident light rays which strike the TIR interface at anglesexceeding the critical angle.

[0024] It is difficult to mechanically frustrate TIR at a non-flatsurface like that formed by the inwardly protruding portions of beads14, due to the difficulty in attaining the required alignment accuracybetween the non-flat surface and the part which is to be mechanicallymoved into and out of optical contact with the surface. However,electrophoretic medium 20 easily flows to surround the inwardlyprotruding portions of beads 14, thus eliminating the alignmentdifficulty and rendering practical the approximately hemisphericallysurfaced (“hemi-beaded”) bead:liquid TIR interface described above andshown in FIG. 1A.

[0025] In the FIG. 1A embodiment, the refractive index of beads 14 ispreferably identical to that of material 16. In such case, only thehemispherical (or approximately hemispherical) portions of beads 14which protrude into medium 20 are optically significant. Consequently,beads 14 need not be discretely embedded within material 16. Asexplained below, hemispherical (or approximately hemispherical) beadsmay instead be affixed to a substrate to provide a composite sheetbearing a plurality of inwardly convex protrusions with no gaps, orminimal gaps, between adjacent protrusions and having sufficientapproximate sphericity to achieve high apparent brightness through awide angular viewing range.

[0026] It is convenient to explain the invention's wide viewing anglecharacteristic for the case in which the inwardly convex protrusions arehemispheres. FIG. 2 depicts, in enlarged cross-section, a hemisphericalportion 60 of one of spherical beads 14. Hemisphere 60 has a normalizedradius r=1 and a refractive index η₁. A light ray 62 perpendicularlyincident (through material 16) on hemisphere 60 at a radial distance afrom hemisphere 60's centre C encounters the inward surface ofhemisphere 60 at an angle θ₁ relative to radial axis 66. For purposes ofthis theoretically ideal discussion, it is assumed that material 16 hasthe same refractive index as hemisphere 60 (i.e. η₁=η₂), so ray 62passes from material 16 into hemisphere 60 without refraction. Ray 62 isrefracted at the inward surface of hemisphere 60 and passes intoelectrophoretic medium 20 as ray 64 at an angle θ₂ relative to radialaxis 66.

[0027] Now consider incident light ray 68 which is perpendicularlyincident (through material 16) on hemisphere 60 at a distance$a_{c} = \frac{\eta_{3}}{\eta_{1}}$

[0028] from hemisphere 60's centre C. Ray 68 encounters the inwardsurface of hemisphere 60 at the critical angle θ_(c) (relative to radialaxis 70), the minimum required angle for TIR to occur. Ray 68 isaccordingly totally internally reflected, as ray 72, which againencounters the inward surface of hemisphere 60 at the critical angleθ_(c). Ray 72 is accordingly totally internally reflected, as ray 74,which also encounters the inward surface of hemisphere 60 at thecritical angle θ_(c). Ray 74 is accordingly totally internallyreflected, as ray 76, which passes perpendicularly through hemisphere 60into the embedded portion of bead 14 and into material 16. Ray 68 isthus reflected back as ray 76 in a direction approximately opposite thatof incident ray 68.

[0029] All light rays which are perpendicularly incident on hemisphere60 at distances a≦a_(c) from hemisphere 60's centre C are reflectedback, as described above for rays 68, 76; it being understood that FIG.2 depicts a theoretically ideal but practically unattainable optically“perfect” hemisphere 60 which reflects ray 76 in a direction oppositethat of incident ray 68. Returning to FIG. 1A, it can be seen that ray30, which is reflected back as ray 42, is another example of such a ray.FIGS. 3A, 3B and 3C depict three of optically “perfect” hemisphere 60'sreflection modes. These and other modes coexist, but it is useful todiscuss each mode separately.

[0030] In FIG. 3A, light rays incident within a range of distancesa_(c)<a≦a₁ undergo TIR twice (the 2-TIR mode) and the reflected raysdiverge within a comparatively wide arc φ₁ centred on a directionopposite to the direction of the incident light rays. In FIG. 3B, lightrays incident within a range of distances a, <a<a₂ undergo TIR threetimes (the 3-TIR mode) and the reflected rays diverge within a narrowerarc φ₂<φ₁ which is again centred on a direction opposite to thedirection of the incident light rays. In FIG. 3C, light rays incidentwithin a range of distances a₂<a≦a₃ undergo TIR four times (the 4-TIRmode) and the reflected rays diverge within a still narrower arc φ₃<φ₂also centred on a direction opposite to the direction of the incidentlight rays. Hemisphere 60 thus has a “semi-retro-reflective”, partiallydiffuse reflection characteristic, causing display 10 to have a diffuseappearance akin to that of paper.

[0031] Display 10 also has a relatively high apparent brightnesscomparable to that of paper. At normal incidence, the reflectance R ofhemisphere 60 (i.e. the fraction of light rays incident on hemisphere 60that reflect by TIR) is given by$R = {1 - \left( \frac{\eta_{3}}{\eta_{1}} \right)}$

[0032] where η₁ is the refractive index of hemisphere 60 and η₃ is therefractive index of the medium adjacent the surface of hemisphere 60 atwhich TIR occurs. Thus, if hemisphere 60 is formed of a lower refractiveindex material such as polycarbonate (η₁˜1.59) and if the adjacentmedium is Fluorinert (η₃˜1.27), a reflectance R of about 36% isattained, whereas if hemisphere 60 is formed of a high refractive indexnano-composite material (η₁˜1.92) a reflectance R of about 56% isattained. When illumination source S (FIG. 1B) is positioned behindviewer V's head, the apparent brightness of display 10 is furtherenhanced by the aforementioned semi-retro-reflective characteristic, asexplained below.

[0033] As shown in FIGS. 4A-4G, hemisphere 60's reflectance ismaintained over a broad range of incidence angles, thus enhancingdisplay 10's wide angular viewing characteristic and its apparentbrightness. For example, FIG. 4A shows hemisphere 60 as seen fromperpendicular incidence that is, from an incidence angle offset 0° fromthe perpendicular. In this case, the portion 80 of hemisphere 60 forwhich a≦a_(c) appears as an annulus. The annulus is depicted as white,corresponding to the fact that this is the region of hemisphere 60 whichreflects incident light rays by TIR, as aforesaid. The annulus surroundsa circular region 82 which is depicted as dark, corresponding to thefact that this is the non-reflective region of hemisphere 60 withinwhich incident rays do not undergo TIR. FIGS. 4B-4G show hemisphere 60as seen from incidence angles which are respectively offset 15°, 30°,45°, 60°, 75° and 90° from the perpendicular. Comparison of FIGS. 4B-4Gwith FIG. 4A reveals that the observed area of reflective portion 80 ofhemisphere 60 for which a≦a_(c), decreases only gradually as theincidence angle increases. Even at near glancing incidence angles (FIG.4F) an observer will still see a substantial part of reflective portion80, thus giving display 10 a wide angular viewing range over which highapparent brightness is maintained.

[0034]FIGS. 5A and 5B further describe the nature of display 10'ssemi-retro-reflective characteristic. “True retro-reflection” occurswhen the reflected ray is returned in a direction opposite to that ofthe incident ray. For purposes of this invention,“semi-retro-reflection” occurs when the reflected ray is returned in adirection approximately opposite to that of the incident ray.Hemispherical reflectors are inherently semi-retro-reflective. In FIG.5A, curve 84 represents the angular range of deviation from trueretro-reflection of light rays reflected by hemisphere 60 afterundergoing TIR twice (the FIG. 3A 2-TIR mode). As expected, the angulardeviation is 0° at$a = {\frac{1}{\sqrt{2}} = {{.707} = {\sin \quad 45{{^\circ}.}}}}$

[0035] That is, in the 2-TIR mode, true retro-reflection occurs if theincident ray encounters hemisphere 60's TIR interface at an angle of45°. The angular deviation ranges from about −10° to about 27° as raysvary over the 2-TIR mode incident range for which they are reflectedtwice. Within this range, apart from the special case of trueretro-reflection at 0° angular deviation, the rays aresemi-retro-reflected.

[0036]FIG. 5A's curve 86 represents the angular range of deviation fromtrue retro-reflection of light rays reflected by hemisphere 60 afterundergoing TIR three times (the FIG. 3B 3-TIR mode). As expected, theangular deviation is 0° at$a = {\frac{\sqrt{3}}{2} = {{.866} = {\sin \quad 60{{^\circ}.}}}}$

[0037] That is, in the 3-TIR mode, true retro-reflection occurs if theincident ray encounters hemisphere 60's TIR interface at an angle of60°. The angular deviation ranges from about −27° to about 18° as raysvary over the 3-TIR mode incident range for which they are reflectedthree times. Within this range, apart from the special case of trueretro-reflection at 0° angular deviation, the rays aresemi-retro-reflected.

[0038]FIG. 5A's curve 87 represents the angular range of deviation fromtrue retro-reflection of light rays which are reflected by hemisphere 60after undergoing TIR four times (the FIG. 3C 4-TIR mode). The angulardeviation is 0° at a=0.924=sin 67.5°. That is, in the 4-TIR mode, trueretro-reflection occurs if the incident ray encounters hemisphere 60'sTIR interface at an angle of 67.5°. The angular deviation ranges fromabout −20° to about 15° as rays vary over the 4-TIR mode incident rangefor which they are reflected four times. Within this range, apart fromthe special case of true retro-reflection at 0° angular deviation, therays are semi-retro-reflected.

[0039]FIG. 5A also depicts curves representing the angular range ofdeviation from true retro-reflection of light rays which are reflectedby hemisphere 60 after undergoing TIR five, six, seven or more times.Instead of considering these 5-TIR, 6-TIR, 7-TIR and higher modes, it ismore useful to consider FIG. 5B, which shows the relative amount(amplitude) of light reflected by hemisphere 60 as a function of theaforementioned angular deviation. The total area beneath the curveplotted in FIG. 5B corresponds to the cumulative energy of light raysreflected by hemisphere 60 in all TIR modes.

[0040] Every curve plotted in FIG. 5A intersects the 0° angulardeviation horizontal axis. Consequently, the cumulative amount of lightreflected in all TIR modes reaches a maximum value at 0° angulardeviation, as seen in FIG. 5B. The cumulative amount of light reflectedin all TIR modes decreases as the magnitude of the aforementionedangular deviation increases, as is also shown in FIG. 5B. Very roughly,approximately one-half of the cumulative reflective energy of light raysreflected by hemisphere 60 lies within an angular deviation range up toabout 10°; and, approximately one-third of the cumulative reflectiveenergy lies within an angular deviation range up to about 5°.Consequently, display 10 has very high apparent brightness when thedominant source of illumination is behind the viewer, within a smallangular range. This is further illustrated in FIG. 1B which depicts thewide angular range α over which viewer V is able to view display 10, andthe angle β which is the angular deviation of illumination source Srelative to the location of viewer V. Display's 10's high apparentbrightness is maintained as long as β is not too large, with thefall-off occurring in proportion to the relative amplitude plotted inFIG. 5B.

[0041] Although it may be convenient to fabricate display 10 usingspherically (or hemispherically) shaped glass beads as aforesaid, asphere (or hemisphere) may not be the best shape for beads 14 in allcases. This is because, as shown in FIG. 6A, even if spherical (orhemispherical) beads 14 are packed together as closely as possiblewithin monolayer 18 (FIG. 1A), gaps 78 unavoidably remain betweenadjacent beads. Light rays incident upon any of gaps 78 are “lost”, inthe sense that they pass directly into electrophoretic medium 20,producing undesirable dark spots on viewing surface 17. While thesespots are invisibly small, and therefore do not detract from display10's appearance, they do detract from viewing surface 17's net averagereflectance.

[0042]FIG. 6B depicts alternative “approximately hemispherical”,inwardly convex “hemi-beads” 14A which are substantially hexagonal in anoutwardmost cross-sectional region parallel to the macroscopic plane ofdisplay 10's viewing surface 17 (FIG. 1A), allowing hemi-beads 14A to bepacked closely together with no gaps, or minimal gaps, between adjacentones of hemi-beads 14A. The inwardmost regions of hemi-beads 14A,(“inward” again being the side of hemi-beads 14A which protrudes intomedium 20) are semi-spherical, as indicated by the innermost circulartopographic lines on hemi-beads 14A. Between their semi-sphericalinwardmost regions and their hexagonal outwardmost regions, the shape ofeach bead hemi-14A varies from semi-spherical to hexagonal, as indicatedby the intermediate topographic lines on hemi-beads 14A. The closer aparticular region of hemi-bead 14A is to the inwardmost semi-sphericalregion, the more spherical that particular region's shape is.Conversely, the closer a particular region of hemi-bead 14A is to theoutwardmost hexagonal region, the more hexagonal that particularregion's shape is.

[0043] Although hemi-beads 14A may have a slightly reduced reflectanceand may exhibit slightly poorer semi-retro-reflection characteristics,this may be more than offset by the absence of gaps. Hemi-beads 14A mayhave many other alternative irregular shapes yet still achieveacceptably high apparent brightness throughout acceptably wide angularviewing ranges. Useful shapes include those which are approximatelyhemispherical (“hemi-beads”), in the sense that such a shape's surfacenormal at any point differs in direction from that of a similarly sized“perfect” hemisphere by an error angle ε which is small. This isillustrated in FIGS. 7A and 7B.

[0044] The solid line portion of FIG. 7A depicts a shape 88 which is not“approximately hemispherical”, even though it closely matches thedimensions of a substantially identically-sized notionally “perfect”hemisphere 90 shown in dashed outline and superimposed on shape 88.Shape 88 has a surface normal 92 at a selected point 94 on shape 88.Hemisphere 90 has a surface normal 96 (i.e. radius) at notional point98, which is the closest point on hemisphere 90 to selected point 94 (inthis example, points 94, 98 happen to coincide at a point where shape 88intersects hemisphere 90). Surface normals 92, 96 differ in direction bya relatively substantial error angle ε₁. By contrast, the solid lineportion of FIG. 7B depicts a hemi-bead 98 which is “approximatelyhemispherical”. Hemi-bead 98 has a surface normal 100 at a selectedpoint 102 on hemi-bead 98. The dashed line portion of FIG. 7B depicts anotional “perfect” hemisphere 104 having a size substantially identicalto and superimposed on hemi-bead 98. Hemisphere 104 has a surface normal106 (i.e. radius) at notional point 108, which is the closest point onhemisphere 104 to selected point 102. Surface normals 100, 106 differ indirection by a relatively insubstantial error angle ε₂ which ispreferably less than 10° and ideally substantially less than 10°.

[0045] As previously mentioned, instead of partially embedding spherical(or approximately spherical) beads in a material, one may instead formhemispherical (or approximately hemispherical) beads on a substrate toprovide a composite sheet bearing a plurality of inwardly convexprotrusions with no gaps, or minimal gaps, between adjacent protrusionsand having sufficient approximate sphericity to achieve high apparentbrightness through a wide angular viewing range. Specifically, highrefractive index hemispherical (or approximately hemispherical) beadsmay be affixed to a low refractive index transparent substrate (i.e.η₁>>η₂, for example η₁≈1.92 and η₂≈1.59) to provide a high apparentbrightness, wide angular viewing range display in accordance with theinvention. Fabrication of such a display is illustrated in FIGS. 8A-8F.

[0046] As shown in FIG. 8A, a large number of the aforementioned highrefractive index T-4 Sign Beads 110 of varying sizes (as supplied by themanufacturer) are pressed into the surface of an adhesive elastomericsubstrate 112, producing a beaded structure 114. A predetermined uniformpressure suffices to embed one-half of a sphere in an elastomer,independently of the sphere's size. Accordingly, application of apredetermined uniform pressure embeds one-half of most of spheres 110 insubstrate 112, as shown in FIG. 8A. Provision of spheres 110 in varyingsizes is advantageous, in that a greater net coverage area can beattained than with spheres of identical size.

[0047] Next, as shown in FIG. 8B, beaded structure 114 is pressed ontoand reciprocated against flat optical polishing surface 116 (for example1 micron diamond grit embedded in brass) as indicated by double-headedarrow 118 (FIGS. 8B and 8C), until spheres 110 are abraded to the pointthat only hemispheres 120 remain embedded in elastomeric substrate 112,with polished, substantially flat, substantially coplanar circular faces122 exposed (FIG. 8D). Faces 122 are then adhered (for example, using aspin-coated ultra-violet cured epoxy) to a transparent flat substrate124 such as polycarbonate (η˜1.59) (FIG. 8E), and elastomeric substrate112 is removed, for example by means of a suitable solvent, yielding thedesired hemi-beaded structure 126 (FIG. 8F) consisting of highrefractive index hemispherical (or approximately hemispherical) beads120 on transparent substrate 124. Structure 126 can then beindium-tin-oxide (ITO) coated to produce a transparent electrode onbeads 120, as previously mentioned. Alternatively, spheres 110 can beITO-coated before they are pressed into substrate 112, then hemispheres120 can be electrically connected to one another by depositing, aroundtheir bases a thin conductive coating such as Bayer Baytron™ conductivepolymer.

[0048] High apparent brightness, wide angular viewing range displays canalso be produced in accordance with the invention by selectablyfrustrating TIR in alternative ways. For example, instead of suspendingabsorptive particles 26 in electrophoresis medium 20, one could suspendan electrode-bearing membrane in the medium as disclosed in WO01/37627which is incorporated herein by reference. TIR can also be selectablyfrustrated without using electrophoresis and without providing anyliquid adjacent the “hemi-beaded” TIR interface. For example, asdisclosed in U.S. Pat. Nos. 5,959,777; 5,999,307; and 6,088,013 (all ofwhich are incorporated herein by reference) a member can be controllablydeformed or positioned by hydraulic, pneumatic, electronic,electrostatic, magnetic, magnetostrictive, piezoelectric, etc. meanssuch that the member either is or is not in optical contact with aselected “pixel” portion of the hemi-beaded TIR interface.

What is claimed is:
 1. A reflective display, comprising: (a) a firsttransparent sheet having: (i) an inwardly protruding structure on aninward side of said first sheet, said structure having a refractiveindex greater than about 1.75; (ii) an outward viewing surface; (iii) anintense evanescent wave region at an inward side of said structure; (b)a second sheet spaced inwardly from said first sheet to define areservoir between said first and second sheets; (c) an electrophoresismedium within said reservoir, said medium having a refractive index lessthan about 1.35; (d) a member within said medium; (e) a first electrodeon said inward side of said structure; (f) a second electrode on anoutward side of said second sheet; and, (i) a voltage source coupledbetween said electrodes to apply a voltage across said medium toselectably, electrophoretically move said member into or out of saidintense evanescent wave region.
 2. A display as defined in claim 1, saidfirst sheet further comprising a nano-composite structure of highrefractive index particles suspended in a polymer.
 3. A display asdefined in claim 1, said member further comprising a plurality of lightabsorptive particles suspended in said medium.
 4. A display as definedin claim 1, wherein said medium is a perfluorinated, inated hydrocarbonliquid.
 5. A method of making a reflective display, said methodcomprising: (a) partially embedding a plurality of approximatelyspherical high refractive index beads in one side of an elastomericsubstrate; (b) removing portions of said beads which are not embedded insaid substrate to produce a plurality of approximately hemisphericalhigh refractive index hemi-beads embedded in said substrate, saidhemi-beads having substantially flat, substantially coplanar faces; (c)transparently adhering said hemi-bead coplanar faces to a transparentsubstrate; and, (d) removing said elastomeric substrate.
 6. A method asdefined in claim 5, wherein said partially embedding further comprisesdistributing said plurality of approximately spherical beads over saidside of said elastomeric substrate and applying a predetermined uniformpressure to said approximately spherical beads to embed approximatelyone-half of substantially each one of said approximately spherical beadsin said side of said elastomeric substrate.
 7. A method as defined inclaim 5, wherein said removing portions of said beads further comprisesabrading said portions of said beads which are not embedded in saidsubstrate by reciprocation against a flat optical polishing surface. 8.A method as defined in claim 5, wherein said adhering further comprisestransparent adhesive bonding.
 9. A method as defined in claim 5, whereinsaid adhering further comprises transparent adhesive bonding with atransparent spin-coated ultra-violet cured epoxy.
 10. A method asdefined in claim 5, wherein said removing said elastomeric substratefurther comprises peeling said elastomeric substrate away from saidhemi-beads.
 11. A method as defined in claim 5, wherein said removingsaid elastomeric substrate further comprises dissolving said elastomericsubstrate in a solvent.